True or false: you inherit your genes from your parents.
Mostly true, but not quite. In theory, you do indeed get half of your DNA from your mother and half from your father; but in practice, there's sometimes a third parent as well, random chance. Genes don't always get transmitted as they should: mutations occur.
As a result, it's not true that "genetic" always implies "inherited". A disease, for example, could be entirely genetic, and almost never inherited. Down's syndrome is the textbook example, but it's something of a special case and until recently, it was widely assumed that most disease risk genes were inherited.
He also doesn't mention, as Razib has in several recent posts at Gene Expression that you don't inherit exactly 50% of your genes from each parent because there are unequal sized chunks and some randomness in germline formation and combination process. You can inherit as little as about 45% of your genes from one parent and as much as about 55%, although those are extreme outliers.
None of this has anything to do with a person "taking after" one parent or another, a phenomena due to someone inheriting more obvious and apparent genes from one parent or by inheriting genes that express more from one parent due to dominant/recessive gene patterns for the phenotypes influenced by those genes.
He also isn't talking about true "third parent" situations where an individual is an extremely genetic chimera who can have different DNA in different parts of his or her body, although this phenomena that is probably underdetected because apart from forensic circumstances DNA samples are typically taken only from a single locus.